Human femur: evaluation of mechanical strength by limit analysis

Population aging, especially in the more developed Countries, is an indicator of well-being, nevertheless it poses a number of problems such as, among other, the increasing of bone-related diseases, skeletal fractures and osteoporosis, which affect the health system and have significant economic implications. In the last few decades, several scientific efforts have been made to predict and describe the human bones mechanical behaviour under different loading conditions, see e.g. [1] and references therein. However, the complexity of the bone material depending, in contrast to engineering materials, by several external factors such as age, conditions of growth, type of feeding, environmental and working circumstances, has not allowed scientists to find approaches of general applicability, so that the research in this area is very active. Finding motivation on the above remarks, the present contribution proposes the application, in the above outlined context, of the Limit Analysis Theory, so focusing on the ultimate bone mechanical conditions. A sufficiently accurate and reliable prediction of the peak/collapse load for a human long bone is attained. In particular, a Finite Element (FE) numerical technique, namely the Elastic Compensation Method (ECM), is promoted to address the human femur limit analysis. The ECM is an iterative procedure made of sequences of linear elastic analyses, through which the elastic moduli of the constituent material are systematically varied to simulate the process of stress redistribution arising within the structure suffering an increasing load till the attainment of its strength threshold. The ECM has been applied by the authors in the past to structures made of engineering materials like steel, composites or reinforced concrete [2]. To deal with human bone material, a constitutive model of Tsai-Wu-type in principal stress space is assumed [3], the latter is modelled in 3D and viewed, at a macroscopic level, as a structural element made of a composite anisotropic material. The obtained numerical results, even if at an early stage, when compared with the ones present in literature and obtained via experimental findings, [4], encourage the authors to continue the undertaken research. References 1. Murphy W., Black J., Hasting G., 2016. Handbook of Biomaterial Properties. 2nd Ed. Springer, New York, NY. 2. De Domenico D., Pisano A.A., Fuschi P., 2014. A FE-based limit analysis approach for concrete elements reinforced with FRP bars. Composite Structures, 107, 594-603. 3. Doblaré M., García J.M., Gómez M.J., 2004. Modelling bone tissue fracture and healing: a review. Engineering Fracture Mechanics, 71, 1809-1840. 4. Dall’Ara E., Luisier B., Schmidt R., Pretterklieber M., Kainberger F., Zysset P., Pahr D., 2013. DXA predictions of human femoral mechanical properties depend on the load configuration. Medical Engineering & Physics, 35, 1564-1572.5.